A285855 Number of permutations of [n] with four ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 40, 430, 6300, 62601, 706608, 8985560, 107911760, 1439518696, 20364348576, 304923257184, 4772610024000, 80570363703696, 1409795519233536, 26263500315144192, 511153327733815296, 10464902116976779776, 223154458395064842240, 5010190272214829475840

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..450

Wikipedia, Permutation

Maple

b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
      (p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
      [multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 5)
    end:
a:= n-> coeff(b(n$2, 0), x, 4):
seq(a(n), n=4..25);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]], {x, 0, 4}];
a[n_] := Coefficient[b[n, n, 0], x, 4];
Table[a[n], {n, 4, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Crossrefs

Column k=4 of A285849.

Cf. A285919.

Sequence in context: A007772 A228122 A247408 * A210355 A210348 A055750

Adjacent sequences: A285852 A285853 A285854 * A285856 A285857 A285858

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved